Question: All of the 4th grade teachers and students from Oak went on a field trip to an archaeology museum. Tickets were $$7.50$ each for teachers and $$4.00$ each for students, and the group paid $$47.00$ in total. A few weeks later, the same group visited a natural history museum where the tickets cost $$30.00$ each for teachers and $$12.50$ each for students, and the group paid $$160.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${7.5x+4y = 47}$ ${30x+12.5y = 160}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-30x-16y = -188}$ ${30x+12.5y = 160}$ Add the top and bottom equations together. $ -3.5y = -28 $ $ y = \dfrac{-28}{-3.5}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $ {7.5x+4y = 47}$ to find $x$ ${7.5x + 4}{(8)}{= 47}$ $7.5x+32 = 47$ $7.5x = 15$ $x = \dfrac{15}{7.5}$ ${x = 2}$ You can also plug ${y = 8}$ into $ {30x+12.5y = 160}$ and get the same answer for $x$ ${30x + 12.5}{(8)}{= 160}$ ${x = 2}$ There were $2$ teachers and $8$ students on the field trips.